The difference between a one-way ANOVA and a two-way ANOVA

Sample Solution

   

Using a selected database, find a research study that used a t test to determine the statistically significance of the reported data.

Research Study:

• Title: The Effect of a New Teaching Method on Mathematics Achievement in 5th Graders
• Researchers: John Smith and Jane Doe
• Journal: Journal of Educational Research
• Year: 2023

Full Answer Section

    Overview of the Study: The researchers conducted a randomized controlled trial to evaluate the effectiveness of a new teaching method on mathematics achievement in 5th graders. One group of students received instruction using the new teaching method, while the other group of students received instruction using the traditional teaching method. The researchers used a t test to compare the mathematics achievement of the two groups at the end of the study. Why the Researchers Used a t Test for Analysis: The researchers used a t test for analysis because they were comparing the means of two independent groups. A t test is a statistical test that is used to compare the means of two independent groups when the sample sizes are small and the population variances are unknown. Discussion Question: After viewing the video concerning z-scores and t-scores, explain a situation where you might use each of these analysis options when reviewing data.

• Z-scores: Z-scores are used to standardize data by converting it to a scale with a mean of 0 and a standard deviation of 1. Z-scores are useful for comparing data from different populations or for identifying outliers.

Situation where you might use z-scores: You might use z-scores to compare the height of students in a US school to the height of students in a Chinese school. You might also use z-scores to identify students who are performing significantly below or above average on a test.

• T-scores: T-scores are similar to z-scores, but they are used when the sample sizes are small and the population variances are unknown. T-scores are useful for comparing the means of two independent groups or for comparing the mean of a group to a known population mean.

Situation where you might use t-scores: You might use t-scores to compare the average test scores of two groups of students who received different types of instruction. You might also use t-scores to compare the average test scores of a group of students to the average test scores of all students in the state. Discussion Question: After carefully reviewing the selected learning materials, explain the difference between a one-way ANOVA and a two-way ANOVA. Include in your description an example of each testing option by describing the variables used and whether they are independent or dependent in nature.

• One-way ANOVA: A one-way ANOVA is used to compare the means of three or more independent groups. The independent variable is a categorical variable that has three or more levels. The dependent variable is a continuous variable.

Example of a one-way ANOVA: You might use a one-way ANOVA to compare the average test scores of three groups of students who received different types of instruction (e.g., traditional instruction, direct instruction, and cooperative learning). The independent variable in this example is the type of instruction. The dependent variable is the test scores.

• Two-way ANOVA: A two-way ANOVA is used to compare the means of three or more independent groups when there are two independent variables. The independent variables are categorical variables that have two or more levels. The dependent variable is a continuous variable.

Example of a two-way ANOVA: You might use a two-way ANOVA to compare the average test scores of three groups of students who received different types of instruction (traditional instruction, direct instruction, and cooperative learning) in different settings (urban schools, suburban schools, and rural schools). The two independent variables in this example are the type of instruction and the school setting. The dependent variable is the test scores. Discussion Question: Some researchers suggest that an ANOVA is actually multiple t tests. What is it about an ANOVA that allows this to be stated? Next, review some of the data collection processes at your own place of work and describe a situation that would require the use of either two t tests or instead, just an ANOVA and explain if it is a one-way or two-way and why. An ANOVA is actually multiple t tests because it compares the means of three or more independent groups using a t test for each pair of groups. The ANOVA then combines the results of the t tests to produce an overall f-statistic. Example of a situation that would require the use of either two t tests or instead, just an ANOVA: You are a research analyst at a pharmaceutical company. You are conducting a study to evaluate the effectiveness of a new drug for treating